* Consider the set of all functions from the real number line to the closed unit interval, and define a topology on so that a sequence in converges towards if and only if converges towards for all.

* Consider the set K of all functions ƒ: → satisfying the Lipschitz condition | ƒ ( x ) − ƒ ( y )| ≤ | x − y | for all x, y ∈.

Consider a project that has been planned in detail, including a time-phased spend plan for all elements of work.

Consider the closed intervals for all integers k ; there are countably many such intervals, each has measure 1, and their union is the entire real line.

Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:

* Chapter 7 divides humility into twelve degrees, or steps in the ladder that leads to heaven :( 1 ) Fear God ; ( 2 ) Substitute one's will to the will of God ; ( 3 ) Be obedient to one's superior ; ( 4 ) Be patient amid hardships ; ( 5 ) Confess one's sins ; ( 6 ) Accept oneself as a " worthless workman "; ( 7 ) Consider oneself " inferior to all "; ( 8 ) Follow examples set by superiors ; ( 9 ) Do not speak until spoken to ; ( 10 ) Do not laugh ; ( 11 ) Speak simply and modestly ; and ( 12 ) Be humble in bodily posture.

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider, also, that all English speakers often pronounce ' Z ' where ' S ' is spelled, almost always when a noun ending in a voiced consonant or a liquid is pluralized, for example " seasons ", " beams ", " examples ", etc.

Consider a hypothetical hotel with countably infinitely many rooms, all of which are occupied – that is to say every room contains a guest.

Consider a series-parallel battery arrangement with all good cells, and one becomes shorted or dead:

Consider the category Grp of all groups with group homomorphisms as morphisms.

Consider the class of all regular paths from a point p to another point q.

Consider code that adds two numbers and then multiplies by a third ; in the Cray, these would all be fetched at once, and both added and multiplied in a single operation.

Consider as an example the interaction between a star and a distant galaxy: The error arising from combining all the stars in the distant galaxy into one point mass is negligible.

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider all the possible strings of p symbols, using an alphabet with a different symbols.

Consider the set W of all deductively closed sets of formulas, ordered by inclusion.

Consider a periodic group G with the additional property that there exists a single integer n such that for all g in G, g < sup > n </ sup >

Consider the theory obtained by adding a new constant symbol ε to the language and adjoining to Σ the axiom ε > 0 and the axioms ε < 1 / n for all positive integers n. Clearly, the standard real numbers R are a model for every finite subset of these axioms, because the real numbers satisfy everything in Σ and, by suitable choice of ε, can be made to satisfy any finite subset of the axioms about ε.

Consider, for example, this code segment in the Java programming language as given by ( as well as all other Java code segments ):

Consider the solid ball in R < sup > 3 </ sup > of radius π ( that is, all points of R < sup > 3 </ sup > of distance π or less from the origin ).

Consider the set of all trial probability distributions that encode the prior data.

Consider, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).

Consider the vectors ( functions ) f and g defined by f ( t ) := e < sup > it </ sup > and g ( t ) := e < sup >− it </ sup >.

Consider the space of real-valued functions together with a special point.

Consider the following functions, which demonstrate several kinds of dependencies:

Consider a set of functions f < sub > 1 </ sub >, f < sub > 2 </ sub >,..., f < sub > n </ sub >.

Consider a set of square-integrable functions with values in,

Consider the functions f and g from the natural numbers to the natural numbers defined as follows:

* Consider the Riesz space C < sub > c </ sub >( X ) of all continuous complex-valued functions of compact support on a locally compact Hausdorff space X.

Consider the banach space of essentially-bounded measurable functions within this measure space ( which is clearly independent of the scale of the Haar measure ).

Consider the following pseudocode ( where it is assumed that functions are first-class values ):

Consider the set F of all those holomorphic functions f on the unit disk for which

Consider the Hilbert space X = L < sup > 2 </ sup > 3 of complex-valued square integrable functions on the interval 3.

Consider two functions and.

Consider the following system of first order partial differential equations for unknown functions,, where

Consider the two different functions of who in " Who's the criminal who did this?

Consider a graphics API with functions to,, and.

Consider all patterns in 1D which have translational symmetry, i. e., functions f ( x ) such that for some a > 0, f ( x + a ) = f ( x ) for all x.

Consider the series of delta functions given by

Consider the problem of finding solutions of the form ƒ ( r, θ, φ ) = R ( r ) Y ( θ, φ ).

Consider a sphere S ( r ) with radius r. A point on the sphere is identified by its latitude φ and longitude λ, for which we introduce the random variables Φ and Λ that take values in Ω < sub > 1 </ sub > = respectively Ω < sub > 2 </ sub > =.

Consider a complex scalar field φ, with the constraint that φ < sup >*</ sup > φ = v², a constant.

Consider a scalar quantity φ = φ ( x, t ), where t is understood as time and x as position.